In the xy -plane, what is the y -coordinate of the point of intersection of the graphs of and ?

Question

Accepted Answer

The correct answer is 1. The point of intersection of the graphs of the given equations is the solution to the system of the two equations. Since and , it follows that , or . Applying the distributive property to the left-hand side of this equation yields . Subtracting from and adding 3 to both sides of this equation yields . Factoring the left-hand side of this equation yields . By the zero product property, if , it follows that . Adding 2 to both sides of yields . Substituting 2 for x in either of the given equations yields . For example, substituting 2 for x in the second given equation yields , or . Therefore, the point of intersection of the graphs of the given equations is . The y -coordinate of this point is 1.

Question in-the